Fibrex was established by Hazel and Dick Key over 57 years ago.
Their daughters Ursula, Angela, son Richard and his wife Heather now run the business.
The grower, which houses the national pelargonium and hedera collections, says the event costs a lot to do and it is having a rest in 2018 and will return if not being at the show affects business.
Richard Godard-Key said: "Looking ahead to next year and our show calendar is a little bit different to the norm. With the changes that have been made to the RHS London Shows, these have, rather sadly, become a venue that is no longer suited to us and so we have decided that, for the time being at least, we shall concentrate on our local arenas. Hampton Court Palace Flower Show will be our only show in the south as we are also taking a well earned respite from Chelsea after more than 50 years of showing there."
Fibrex's propagation glasshouse is being replaced, while the nursery plans a 60th anniversary celebration on 16-17 June.
Acceptance letters for Chelsea are due to be sent this week after potential exhibitors applied in August.
Chelsea show manager Tom Harfleet is leaving, while RHS shows director Nick Mattingley is having "unexpected leave". Katherine Potsides is new Chelsea manager, Chelsea's fifth in six years.
Reports suggest there are more Chelsea garden applications than in 2017, when there were eight show gardens, half the number of the previous year.
In the pavilion, Wedgwood took the monument site with a large trade stand to start a three-year partnership. The pottery may have sponsor a show garden in 2018.
A new 'new gardens spaces category' is replacing 'Fresh' gardens, with the HTA/Warnes McGarr and Robert Barker believed to be among applicants.